Characterizing the Separability Gap in Prior-Data Fitted Networks
Prior-data fitted networks (PFNs) are transformers pretrained on simulated datasets to approximate Bayesian posterior predictive distributions. Standard PFN theory assumes a separable task prior, under which the feature distribution and the mechanism generating labels from features are independent. We show that common PFN priors are non-separable, even in simple settings. Consequently, standard pretraining targets a predictive distribution based on a task posterior updated using both the labeled context and the query features. We characterize its difference from the predictive based on the context posterior alone and show that this difference vanishes under posterior concentration. Under ...
| Authors | Julius Kobialka, Manuel Hülskamp, Thomas Nagler et al. |
|---|---|
| Primary category | cs.LG |
| Published | 10 October 2026 |
| Last updated at source | 10 October 2026 |
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